Question

A voltmeter reads $4V$ when connected to a parallel plate capacitor with air as a dielectric. When a dielectric slab is introduced between plates for the same configuration, voltmeter reads $2V$. What is the dielectric constant of the material?

• A. $8$
• B. $2$
• C. $10$
• D. $0.5$

Answer 1

Answer: (B)

For a capacitor with dielectric, capacitance is given by:

$C=\frac{K{\epsilon }_{o}A}{d}$

From law of conservation of charge, initial and final charge on the capacitor is same.

$Q_i=Q_f$

From definition of capacitance,

$C_i{V}_i=C_f{V}_f$

$\frac{{\epsilon }_{o}A}{d}{V}_i=\frac{K{\epsilon }_{o}A}{d}{V}_f$

$4=2K$

$K=2$